Finite dimensional realization of fractional Tikhonov regularization method in Hilbert scales

Abstract

One of the intuitive restrictions of infinite dimensional Fractional Tikhonov Regularization Method (FTRM) for ill-posed operator equations is its numerical realization. This paper addresses the issue to a considerable extent by using its finite dimensional realization in the setting of Hilbert scales. Using adaptive parameter choice strategy, we choose the regularization parameter and obtain an optimal order error estimate. Also, the proposed method is applied to the well known examples in the setting of Hilbert scales.

Keywords

• Ill-posed problem
• Finite dimensional Fractional Tikhonov regularization
• Hilbert scales
• Adaptive parameter choice strategy